Advanced process control (APC) models for semiconductor manufacturing enable the reduction of process variability in semiconductor manufacturing processes. Two types of models utilized for APC include a feedback list approach and a state-based approach.
In the feedback list scenario, data at metrology upload is stored in a list sorted by process tool lot order. When a setting calculation is desired, the system performs the model update calculations on this list of values (e.g., an exponentially weighted moving average (EWMA) calculation to filter out the effect of noise). However, at no point is this calculated value stored back for use when the next lot arrives for processing. The model update calculation is repeated each time on this list of values only.
As a result, the feedback list approach cannot correctly deal with models requiring terms that depend on different contexts (i.e., partitions). The feedback list approach thereby results in a uniform partitioning structure. An excessively large number of partitions and APC performance deterioration may be a consequence due to data being binned across such a large number of partitions. In view of that, individual partitions are not updated frequently enough with new data to keep track of the process drift for controlling variability in the semiconductor processing system.
This former shortcoming makes the feedback list approach non-optimal in high-mix manufacturing, as it results in infrequent updates to low volume partitions and, accordingly, the need to run a large number of send-aheads. However, the feedback list approach does provide good support for handling issues such as re-measurement at metrology, data invalidation, and, if needed, enforcement of model updates to follow the order of processing. These are the primary reasons the feedback list approach is used for APC applications.
In the state-based APC model scenario, correct implementation of APC models that have different partitioning structures based on the components of variation may be achieved. State-based models offer a natural representation for tracking multiple sources of variation. In addition, the update algorithms used for these models are easier to tune than the feedback list approach (as state-based models follow the infinite form representation versus the finite form supported by feedback lists).
One way that state-based models accomplish these improvements over the feedback list approach is by providing for updating in the feedback path. However, updating in the feedback path can result in model update errors in the presence of re-measurements at metrology and data invalidations. Model update errors also arise in the state-based approach due to the fact that the update is in the order of metrology instead of the order of processing. These shortcomings make state-based APC models less robust in the semiconductor manufacturing domain.
Currently, there is no known solution for handling re-measurements and data invalidations for state-based APC models. This forces APC problems to be cast in the context of a feedback list, which, as discussed above, can be less desirable for implementation than the state-based APC models. A state-based APC model that can correctly handle re-measurements, data invalidation, and sequence updates in the order of processing to more accurately compute APC settings on the process tool would be beneficial.